EXERGY, ENERGY SYSTEM ANALYSIS AND OPTIMIZATION – Vol. I - Exergy Balance and Exergetic Efficiency - G.
Tsatsaronis and F. Cziesla
EXERGY BALANCE AND EXERGETIC EFFICIENCY
G. Tsatsaronis and F. Cziesla
Institute for Energy Engineering, Technische Universität Berlin, Germany
Keywords: Exergy Balance, Exergy Destruction, Exergy Loss, Exergetic Efficiency,
Guidelines for Rational Energy Use, Thermodynamic Inefficiencies.
Contents
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1. Exergy Balance and Exergy Destruction
1.1. Closed System Exergy Balance
1.2. Control Volume Exergy Balance
1.3. Thermodynamic Inefficiencies
1.3.1. Exergy Destruction Associated With Heat Transfer
1.3.2. Exergy Destruction Associated With Friction
1.3.3. Avoidable and Unavoidable Exergy Destruction
1.3.4. Endogenous and Exogenous Exergy Destruction
1.4. Guidelines for improving the Use of Energy Resources
2. Exergetic Variables
2.1. Exergetic Efficiency
2.2. Exergy Destruction and Exergy Loss
2.3. Exergy Destruction Ratio
Glossary
Bibliography
Biographical Sketches
Summary
For the evaluation and improvement of thermal systems, it is essential to understand the
sources of thermodynamic inefficiencies and the interactions among system
components. All real energy conversion processes are irreversible due to effects such as
chemical reaction, heat transfer through a finite temperature difference, mixing of
matter at different compositions or states, unrestrained expansion, and friction. Exergy
balances assist in calculating the exergy destruction within system components. Thus,
the thermodynamic inefficiencies and the processes that cause them are identified. Only
a part of the thermodynamic inefficiencies can be avoided by using the best currently
available technology. Improvement efforts should be centered on avoidable
inefficiencies. Dimensionless variables are used for performance evaluations. An
appropriately defined exergetic efficiency unambiguously characterizes the performance
of a system from the thermodynamic viewpoint.
1. Exergy Balance and Exergy Destruction
All thermodynamic processes are governed by the laws of conservation of mass and
energy. These conservation laws state that mass and energy can neither be created nor
destroyed in a process. Exergy, however, is not conserved but is destroyed by
irreversible processes within a system. Consequently, an exergy balance must contain a
©Encyclopedia of Life Support Systems (EOLSS)
EXERGY, ENERGY SYSTEM ANALYSIS AND OPTIMIZATION – Vol. I - Exergy Balance and Exergetic Efficiency - G.
Tsatsaronis and F. Cziesla
destruction term, which vanishes only in a reversible process. Furthermore, exergy is
lost, in general, when a material or energy stream is rejected to the environment.
1.1. Closed System Exergy Balance
The change in total exergy ( Esys ,2 − Esys ,1 ) of a closed system caused through transfers
of energy by work and heat between the system and its surroundings is given by
Esys ,2 − Esys ,1 = Eq + Ew − ED .
(1)
The exergy transfer Eq associated with heat transfer Q is
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2⎛
T ⎞
Eq = ∫ ⎜1 − 0 ⎟ δQ ,
1
⎝ Tb ⎠
(2)
where Tb is the temperature at which the heat transfer crosses the system boundary.
The exergy transfer Ew associated with the transfer of energy by work W is given by
Ew = W + p0 (V2 − V1 ) .
(3)
The last term in Eq. (3) accounts for non-useful work done either by the surroundings,
or on the surroundings. For example, in a process in which the system volume increases
(V2 > V1 ) , the work p0 (V2 − V1 ) being done by the system on the surroundings is not
useful.
A part of the exergy supplied to a real thermal system is destroyed due to irreversible
processes within the system. The exergy destruction ED is equal to the product of
entropy generation S gen within the system and the temperature of the reference
environment T0 .
ED = T0 S gen ≥ 0 .
(4)
Hence, the exergy destruction can be calculated either from the entropy generation
using an entropy balance or directly from an exergy balance (Eq. (1)). ED is equal to
zero only in an ideal reversible process.
©Encyclopedia of Life Support Systems (EOLSS)
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EXERGY, ENERGY SYSTEM ANALYSIS AND OPTIMIZATION – Vol. I - Exergy Balance and Exergetic Efficiency - G.
Tsatsaronis and F. Cziesla
Figure 1: Schematic diagram to illustrate the exergy balance for a control volume
system.
1.2. Control Volume Exergy Balance
An exergy transfer across the boundary of a control volume system can be associated
with either a material stream or an energy transfer by work or heat. The general form of
the exergy balance for a control volume system involving multiple inlet and outlet
streams of matter and energy (Figure 1) is
dEcv,sys
dt
nq ⎛
⎛ nw
T ⎞
dV ⎞
= ∑ ⎜1 − 0 ⎟ Q j + ⎜ ∑ W j + p0 cv ⎟
⎜ Tj ⎟
⎜
dt ⎟⎠
j =1 ⎝
⎠ ⎝ j =1
E q , j
,
r
p
j =1
j =1
(5)
+ ∑ Ei , j − ∑ Ee, j − E D
where Ei , j and Ee, j are the total exergy transfer rates at the inlet and outlet, respectively
(see Basic Exergy Concepts for the total, physical, chemical, kinetic, and potential
exergy associated with mass transfers). The term Q j represents the time rate of heat
transfer at the location on the boundary where the temperature is T j . The associated rate
of exergy transfer E is given by
q, j
⎛ T ⎞
Eq, j = ⎜1 − 0 ⎟ Q j .
⎜ Tj ⎟
⎝
⎠
©Encyclopedia of Life Support Systems (EOLSS)
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EXERGY, ENERGY SYSTEM ANALYSIS AND OPTIMIZATION – Vol. I - Exergy Balance and Exergetic Efficiency - G.
Tsatsaronis and F. Cziesla
For T j > T0 , the exergy rate Eq, j associated with heat transfer is always smaller than the
heat transfer rate Q j . The ratio
E q, j Q j is shown in Figure 2 for different
temperatures T j .
In applications below the temperature of the environment (T j < T0 ), Eq , j and Q j have
opposite signs: When energy is supplied to the system, exergy is removed from it and
T
vice versa. For T < 0 , the absolute value of the exergy transfer E is greater than the
j
q, j
2
heat transfer Q j . In this case, the minimum theoretical useful work to generate Q j is
greater than Q .
j
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Figure 3 illustrates the directions of heat transfer and the associated transfer of exergy in
a heat exchanger operating above and below the temperature of the reference
environment T0 .
The purpose of purchasing and operating the heat exchanger in Figure 3a is to increase
the temperature of cold stream 1. Here, both energy and exergy are supplied to stream 1.
In a heat exchanger operating below the temperature of the environment (Figure 3b,
T j < T0 , j = 1,..., 4) , energy is transferred from the hot stream to the cold stream, but
exergy is transferred from the cold stream to the hot stream ( E > E , E < E ) . Here,
4
3
2
1
the purpose of the heat exchanger is to cool the hot stream (increase its physical
exergy).
Figure 2: Exergy associated with the transfer of heat at different temperatures T j . Here,
the temperature of the environment is T0 = 298.15K .
©Encyclopedia of Life Support Systems (EOLSS)
EXERGY, ENERGY SYSTEM ANALYSIS AND OPTIMIZATION – Vol. I - Exergy Balance and Exergetic Efficiency - G.
Tsatsaronis and F. Cziesla
Figure 3: Heat exchangers operating above (Fig. 3a) and below (Fig. 3b) the
temperature of the reference environment T0 .
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In Figure 1 and Eq. (5) the exergy transfer E w associated with the time rate of energy
transfer by work Wcv other than flow work is
nw
dV
dV
E w = ∑ W j + p0 cv = Wcv + p0 cv .
dt
dt
j =1
(7)
The term E D in Eq. (5) accounts for the time rate of exergy destruction due to
irreversible processes within the control volume. Either the exergy balance (Eq. (5)) or
the relationship E D = T0 Sgen can be used to calculate the exergy destruction within a
control volume system.
Under steady state conditions, Eq. (5) becomes
nq
p
r
j =1
j =1
j =1
0 = ∑ E q , j + Wcv + ∑ Ei , j − ∑ Ee, j − E D .
(8)
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Bibliography
Bejan A., Tsatsaronis G., and Moran M. (1996). Thermal Design and Optimization. New York: John
Wiley & Sons. 542 p. [Contains an introduction to the exergy concept, applications, and exergy-aided
cost minimization of energy conversion systems]
Kotas T.J. (1995). The Exergy Method of Thermal Plant Analysis. Malabar, Florida: Krieger Publishing
Company. 328 p. [Provides a detailed discussion of the exergy concept and its applications.]
©Encyclopedia of Life Support Systems (EOLSS)
EXERGY, ENERGY SYSTEM ANALYSIS AND OPTIMIZATION – Vol. I - Exergy Balance and Exergetic Efficiency - G.
Tsatsaronis and F. Cziesla
Lazzaretto A. and Tsatsaronis G. (1999). On the calculation of efficiencies and costs in thermal systems.
In Aceves S.M., Garimella S., and Peterson R. (eds.), Proceedings of the ASME Advanced Energy
Systems Division, AES-Vol. 39, 421-430, ASME, New York.
Moran M.J. and Shapiro H.N. (2004). Fundamentals of Engineering Thermodynamics. 5th Ed. New York:
John Wiley & Sons. 936 p. [Thermodynamics textbook with an introduction to the exergy concept.]
Sama D.A. (1995). The Use of the Second Law of Thermodynamics in Process Design. J. Eng. Gas
Turbines and Power, 117:179-185, September. [Provides guidelines for improving the use of energy
resources.]
Szargut J., Morris D.R., and Steward F.R. (1988). Exergy Analysis of Thermal, Chemical, and
Metallurgical Processes. New York: Hemisphere, New York, 332 p.[This reference contains useful
information about standard molar chemical exergies and discusses the exergy concept and its
applications.]
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Tsatsaronis G. and Park M.-H. (1999). On Avoidable and Unavoidable Exergy Destructions and
Investment Costs in Thermal Systems. in: Ishida M., Tsatsaronis G., Moran M., and Kataoka H. (Eds.)
Proceedings of the International Conference on Efficiency, Costs, Optimization, Simulation and
Environmental Aspects of Energy Systems (ECOS ’99), June 8-10, Tokyo, pp. 116-121.
Biographical Sketches
Professor Tsatsaronis is the Bewag Professor of Energy Conversion and Protection of the Environment
and the Director of the Institute for Energy Engineering at the Technical University of Berlin, Germany.
He studied mechanical engineering at the National Technical University of Athens, Greece, receiving the
Diploma in 1972. He continued at the Technical University of Aachen, Germany, where he received a
Masters Degree in business administration in 1976, a Ph.D. in combustion from the Department of
Mechanical Engineering in 1977, and a Dr. Habilitatus Degree in Thermo-economics in 1985.
In the last twenty five years he has been responsible for numerous research projects and programs related
to combustion, thermo-economics (exergo-economics), development, simulation and analysis of various
energy-conversion processes (coal gasification, electricity generation, hydrogen production, cogeneration,
solar energy-conversion, oil production in refineries and also from oil shales, carbon black production,
etc) as well as optimization of the design and operation of energy systems with emphasis on power plants
and cogeneration systems.
He is a Fellow of the American Society of Mechanical Engineers (ASME) and a member of the American
Institute of Chemical Engineers, the German Association of University Professors and the Greek Society
of Engineers. He is the Past Chairman of the Executive Committee of the International Centre for Applied
Thermodynamics.
In 1977 he received for his Ph.D. Thesis the Borchers Award from the Technical University of Aachen,
Germany and in 1994 and 1999 the E.F. Obert Best Paper Award from ASME. In 1997 he became a
Honorary Professor at the North China Electric Power University and in 1998 he received from ASME
the James Harry Potter Gold Medal for his work in exergo-economics.
He currently serves as an associate editor of Energy - The International Journal (since 1986), Energy
Conversion and Management (since 1995), International Journal of Applied Thermodynamics (since
1998), and International Journal of Energy, Environment and Economics (since 2001). He co-authored
with A. Bejan and M. Moran the book Thermal Design and Optimization and published over 150 papers.
Dr. Frank Cziesla is Senior Research Associate and Lecturer at the Institute for Energy Engineering,
Technical University of Berlin, Germany.
F. Cziesla received the Diploma in Chemical Engineering from the Technical University of Berlin in
1994. In the same year, he joined the Institute for Energy Engineering as a Ph.D candidate. His research
activities on the design of cost-effective energy conversion systems using exergy-based optimization
techniques and knowledge-based approaches led to the Ph.D. degree in 1999. He spent the summer of
1997 at the School of Nuclear Engineering, Purdue University (USA) working on a combination of
exergy-based optimization techniques and fuzzy systems.
©Encyclopedia of Life Support Systems (EOLSS)
EXERGY, ENERGY SYSTEM ANALYSIS AND OPTIMIZATION – Vol. I - Exergy Balance and Exergetic Efficiency - G.
Tsatsaronis and F. Cziesla
His current research activities focus on the design and operation of cost-effective energy conversion
systems using exergy-based analysis and optimization techniques (thermoeconomics) as well as principles
taken from the fields of artificial intelligence (experts systems) and computational intelligence (fuzzy
systems, evolutionary algorithms).
He lectures on energy engineering, power plant technology, thermal design and optimization as well as
applications of computational intelligence in energy engineering.
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Dr. Cziesla is a member of the German Association of Engineers (VDI, Verein Deutscher Ingenieure) and
the Society for Chemical Engineering and Biotechnology (DECHEMA, Gesellschaft für Chemische
Technik und Biotechnologie e.V.).
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